CAM colloquium - Friday, April 1
3:30 p.m.
655 Rhodes Hall

Speaker: Walter Strauss

 

Title: Periodic Traveling Rotational Water Waves

Abstract: I will consider classical 2D water waves with non-trivial vorticity, under the influence of gravity over a flat bottom. The pressure is constant at
the air-water interface. The motion of the water is described by the Euler equations. Because of the vorticity, they do not reduce to the Laplace equation. The first rotational periodic traveling wave was constructed by Gerstner in 1802. In the intervening two centuries most analyses assumed irrotational flow.

In this lecture I will discuss my joint work with Adrian Constantin regarding periodic traveling waves with arbitrary vorticity functions. There exist global continua of such waves, varying from small to large amplitude. If the vorticity varies monotonically with depth, there is a physically natural variational formulation. Furthermore, some of these waves have intriguing stability properties.

 

Refreshments at 4:30 in 657 Rhodes Hall.